At our new home, we have hard water. I had thought that the teabags I was buying were just weak, but the internet seems to indicate that the hard water will actually change the taste of the tea to a more chalky taste with some residue.

Two suggestions I have come across are either brewing with bottled water (I try to reduce the amount of packaging I buy so don't want to do this), or brewing the tea double strength (this makes it a little bitter).

The two popular pitcher-type filter brands in the US are Brita and Pur. We used to use a Brita, and it worked OK, but it was a constant annoyance to get certain members of the family to refill it - the pitcher was always empty when I wanted some water. We've now gotten an under-sink filter that works much better - it makes the water taste wonderful (as opposed to the Brita, which was always just barely acceptable) and there's no refilling needed.
–
MartiDec 30 '10 at 17:08

We use a brita filter and found that we had to start using it for making coffee, definitely improved the flavor.
–
ManakoJan 3 '11 at 20:26

I recently started using a Brita filter pitcher as well, for coffee and tea. Our well water tastes perfectly fine, but as its hard was leaving deposits in the coffee maker and tea pot. Using filtered water fixed that problem.
–
KeithBJan 5 '11 at 17:54

Put a pinch (a tiny tiny bit--see how little you can pinch) of baking soda in the cup when you put the bag in. It will make your tea strong, and you won't taste the baking soda. It also works with soft water if you are a cheapskate and want to get more tea out of your bags! :)